Hazard analysis of future surface displacements on active faults based on the recurrence interval of strong earthquakes

Qingyun Zhou; Jingnan Liu; Peng Tian; Weidong Luo; Xianfu Bai; Yue Yang; Zhenyu Zou

doi:10.1515/geo-2022-0763

Article Open Access

Hazard analysis of future surface displacements on active faults based on the recurrence interval of strong earthquakes

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Published/Copyright: February 10, 2025

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From the journal Open Geosciences Volume 17 Issue 1

Abstract

Coseismic surface displacements pose a serious threat to the safety of linear infrastructures on active faults. A reasonable evaluation of surface displacements on active faults is important. Probabilistic fault displacement hazard analysis (PFDHA) is often used for surface displacement evaluation. However, PFDHA, developed based on the classical probabilistic method, requires an in-depth study of the activity parameters of all active faults in seismic–tectonic zones, greatly limiting its application in engineering design. The recurrence interval of strong earthquakes is a readily obtainable parameter of fault activity. In this study, we combine this key parameter with various seismic indicators to develop a comprehensive algorithm to assess potential future surface displacement hazards. In addition, the factors affecting the method are analyzed, and the surface displacements of several earthquakes with a magnitude of 7 or above are compared. The results indicate that the predicted future surface displacements using our method are greater than the true displacements of seismic events. For easy use, the exceedance probability–displacement (horizontal and vertical) curves of 27 strong earthquake recurrence intervals are given. This facilitates structural designers to quickly obtain future displacement values in structural design.

Keywords: active fault; probabilistic fault displacement hazard analysis; strong earthquake recurrence interval; seismic design; return period

1 Introduction

The destructive effects of major earthquakes on structures can be divided into two types: First, the ground motion near the faults is significantly higher than that at a distance (known as the “near-fault effect”); second, the surface displacement of the faults can tear apart all structures located above the fault. We can cope with larger ground motion by increasing seismic measures, but simply increasing seismic measures cannot resist the tearing effect of faults. The selection of project sites should follow the principle of “avoiding active faults.” However, in areas with complex faults, linear infrastructures often cannot completely avoid this. For example, the “Yunnan Central Water Diversion Project” in Yunnan, China, and the “China-Myanmar Petroleum Pipeline” both cross nearly ten active faults. If such projects fail to realize the hazard of surface displacement to active faults in design and construction, it will cause serious losses in future earthquakes [1,2,3,4]. As such, a reasonable evaluation of the displacement hazard of active faults has important theoretical significance and application value in engineering construction.

Two methods are often used to estimate the distance of fault surface displacement, but both with relatively large limitations. The first is deterministic evaluation; that is, the maximum potential earthquake magnitude on the active fault is used to estimate the corresponding maximum displacement, and the maximum displacement is assumed to be uniformly distributed along the fault [5,6]. This method does not take into account the uncertainty of key factors such as magnitude distribution, maximum displacement, stress drop, peak acceleration, and rupture length. This results in adopting conservative approaches for displacement resistance in the project, wasting unnecessary manpower, material, and financial resources. The second is the probabilistic evaluation method. The most widely used method is probabilistic fault displacement hazard analysis (PFDHA) [7,8]. The development of the PFDHA algorithm based on classic PSHA requires an in-depth understanding of the activity parameters of the entire fault or even all the faults in the seismotectonic zones [9,10]. The probabilistic methods also have similar requirements (see, e.g., the study of Wu et al. [11]). Based on these methods, if there is an insufficient understanding of the activity parameters of all faults in the seismotectonic zones, the reliability of the obtained results will be low.

In fact, the probabilistic evaluation method invests high cost and longtime in studying the activity parameters of the target and surrounding faults to obtain more accurate future displacement. The deterministic evaluation method achieves sufficient displacement on the fault and increases engineering costs in design and construction, which cannot meet the needs of scientific defense of fault surface displacement or construction organization. Construction organization generally hopes to achieve a balance between “time and cost” and “accuracy of future displacement of faults,” that is, obtain a high accuracy of surface displacement with a certain amount of research.

Multiple activity parameters can be used to describe the activity characteristics of active faults and predict the surface displacement hazard of faults, such as the latest activity era, slip rate, elapsed time of strong earthquakes, recurrence interval of strong earthquakes, unbroken segment, and locking depth [12,13,14]. In these parameters, the recurrence interval of strong earthquakes is the most important and relatively easy to obtain. Combined trench surveying with chronological testing methods, the recurrence interval of strong earthquakes at a certain point on the active fault was obtained to be about 10,000–20,000 dollars [15,16]. Based on the recurrence interval of strong earthquakes on active faults and the probabilistic evaluation method, a simple and reliable estimation method for fault surface displacement is investigated. This method is expected to provide theoretical support for the evaluation of fault displacement resistance parameters of linear infrastructures crossing active faults.

2 Methods

2.1 Methods for estimating future displacements

The seismicity on the active faults follows the revised magnitude–frequency relationship:

(1) log 10 N ( m ) = a − b M ,

where b reflects the relationship between the quantity of earthquakes with different magnitudes in a certain space. b is different at different regions, and even in the same region, b calculated by different researchers may also be different. For example, Liu et al. [17] reported that b in Yunan was between 0.75 and 0.85. In the “Seismic ground motion parameters zonation map of China” [18], b in Yunnan Province and the surrounding areas was 0.8. Zhang [19] obtained a b-value of 0.7 in Yunnan by relocation. Here, b = 0.8.

The recurrence interval of strong earthquakes on the fault obtained through the paleoseismic method is T. The upper limit of the magnitude of the fault is m _uz, and the lower limit of the magnitude that may cause surface displacement is m ₀. The annual average incidence of earthquakes between m ₀ and m _uz is as follows:

(2) ν 0 = 1 / T ,

m ₀ and m _uz are two parameters that have a great influence on the model. Huang [20] made statistics on surface displacement earthquakes in the Chinese mainland. In these earthquakes, more than 90% had ≥7 magnitudes. Therefore, this study suggests that earthquakes with a magnitude of ≥7 will cause surface displacement. The magnitudes of paleoearthquakes recorded in paleoseismic trenches are ≥7. Therefore, m ₀ is taken as 7.0. The magnitudes of earthquakes within the first-order continental plate are usually not greater than 8.5. Therefore, m _uz is taken as 8.5.

Assuming that the time course of earthquakes within an active fault follows a segmented Poisson process, the probability of n earthquakes occurring on the fault in year t is as follows:

(3) P ( n ) = ( ν 0 t ) n n ! e − v 0 t .

The corresponding magnitude probability density function is as follows:

(4) f ( m ) = β exp [ − β ( m − m 0 ) ] 1 − exp [ − β ( m uz − m 0 ) ] ,

where β = bln10. In actual work, the magnitude m is divided into Nm bins, where m _j represents the magnitude bin in the magnitude range (m _j ± Δm/2). Then, the annual incidence of a m _j-file earthquake within the fault is as follows:

(5) P ( m i ) = 2 β f ( m j ) ⋅ sinh 1 2 β Δ m .

The number of m _j earthquakes that will occur on the fault in the next t-year is as follows:

(6) n i ( t ) = P ( m i ) ⋅ ν 0 ⋅ t .

Historical earthquake statistics show that surface displacements caused by earthquakes of different magnitudes are also different, and the displacement distance is positively correlated with the earthquake magnitude. The number of earthquakes with a displacement distance greater than d in the next year t is as follows:

(7) m ( d , t ) = ∑ i q i ( d ) ⋅ n i ( t ) ,

where q _i(d) is the conditional probability that surface displacements caused by a m _i magnitude earthquake exceed level d. We consider that the probability of these m(d,t) earthquakes occurring in the next t year does not change over time, and then the probability of an event exceeding the surface displacement d in the next t year is as follows:

(8) P ( d , t ) = 1 − exp [ − m ( d , t ) ] .

2.2 Statistical relationship between surface displacements and magnitude

Due to the differences in sample selection, the statistical relationships between surface displacements and magnitude obtained by different researchers are often different. We select the statistical relationship obtained by Huang [20] based on earthquakes in the Chinese mainland. A total of 46 horizontal displacements and 39 vertical displacements were collected by Huang [20]. The least-squares method is used for regression analysis. The regression formula is as follows:

(9) lg D h = − 3.1310 + 0.4869 Ms , R = 0.5613 , σ = 0.1291 , n = 46 ,

(10) lg D v = − 2.8919 + 0.4207 Ms , R = 0.4747 , σ = 0.1611 , n = 39 .

2.3 Method for the acquisition of strong earthquake recurrence interval

The concept of “recurrence interval” is widely used for hazard assessment in seismology [21]. The more common methods for determining recurrence intervals include paleoseismology, seismology, and geodetic methods [22,23]. The recurrence intervals derived from different methods have distinct implications. We pay more attention to the recurrence intervals of strong earthquakes that may cause surface displacements. The recurrence intervals obtained from paleoseismology largely correspond to those of strong earthquakes capable of generating surface displacements. Therefore, the recurrence intervals derived from paleoseismology are more suitable for the study of surface displacement hazards.

Paleoseismology [24] obtains the relationship between faults and strata through methods such as trenching and drilling and then uses dating methods such as Carbon-14, Chlorine-36, Optical dating, REEs, and bioluminescence (see, e.g., previous studies [25,26]) to determine the timing of paleoearthquakes. This is currently the mainstream and reliable method for obtaining recurrence intervals of strong earthquakes in earthquake engineering. The history of seismic records is relatively short compared with the recurrence interval of strong earthquakes. For example, China and Italy have the longest history of seismic records, with 2,000–3,000 years, and the recurrence interval of strong earthquakes on active faults is generally several to tens of thousands of years. With such a long recurrence interval, even with China’s 3,000-year historical seismic record, its time span is still only one part of the earthquake recurrence interval. Therefore, the sequences of strong earthquakes occurring on major active faults are obtained using paleoseismic research methods.

3 Results

In the seismic fortification design of bridges and tunnels in Chinese mainland, the E2 seismic action, that is, the return periods most concerned by designers are 2,000, 1,000, and 475 years (their corresponding exceedance probabilities are about 5% and 10% in 100 years, and 10% in 50 years). Using the method described in the previous section, the horizontal and vertical displacements are calculated for different exceedance probabilities under four recurrence intervals of active faults. The results are shown in Figure 1. The four lines represent active faults with different activity intensities: the red, green, blue, and black lines represent the active faults with recurrence intervals of 1,000, 2,000, 5,000, and 10,000 years, respectively. There was only one earthquake event during the entire Holocene period for faults with a recurrence interval of 10,000 years.

Figure 1

(a) Horizontal displacement and (b) vertical displacement. The red, green, blue, and black lines represent the active fault with a recurrence interval of 1,000, 2,000, 5,000, and 10,000 years, respectively. The dotted line represents the exceedance probability, which is of greater concern in engineering design. The numbers above the dotted line are the recurrence intervals of strong earthquakes corresponding to the exceedance probability. Other parameters used in the calculation are b = 0.8, m ₀ = 7, and m _uz = 8.5.

For ease of use, we list the horizontal displacements and vertical displacements corresponding to some important exceedance probabilities (recurrence intervals) of Figure 1, as shown in Table 1. Based on the above results, we can draw the following conclusions:

For the Holocene faults with a recurrence interval of strong earthquakes greater than or equal to 10,000 years, this type of fault cannot generate surface rupture. Whether it is a bridge or a tunnel, the possibility of surface displacement does not need to be considered in the second-stage seismic design (Earthquake action E2). The possibility of surface displacement only needs to be considered when the E2 recurrence interval of a project is close to or exceeds 10,000 years;
For Holocene faults with a recurrence interval of strong earthquakes of approximately 5,000 years, only particularly important bridges and tunnels (with an E2 return period close to or greater than 5,000 years) need to consider surface displacement. When the recurrence interval of strong earthquakes on the fault is lower than 2,000 years, the hazard of surface displacement needs to be taken into account;
Assuming the return period of E2 in the construction project is T1, and the recurrence interval of strong earthquakes on active faults is T2, when T1 ≥ T2, the hazard of surface horizontal and vertical displacements needs to be considered. It should be noted that in the present study, a 7-magnitude earthquake is used as the minimum magnitude (m ₀) for an earthquake that causes surface rupture. When introducing a 7-magnitude earthquake into equations (9) and (10), the displacements obtained are 1.9 and 1.1 m, respectively. Therefore, in the calculation results, there will be no displacement lower than these two figures.

Table 1

Horizontal and vertical displacements at the surface under four recurrence intervals and five exceedance probabilities of active faults

Recurrence interval (a)	Horizontal displacement (m)					Vertical displacement (m)
Recurrence interval (a)	100a 1%	100a 2%	100a 5%	100a 10%	50a 10%	100a 1%	100a 2%	100a 5%	100a 10%	50a 10%
10,000	2.00	—	—	—	—	1.19	—	—	—	—
5,000	2.95	2.00	—	—	—	1.66	1.19	—	—	—
2,000	4.68	3.31	2.00	—	—	2.45	1.84	1.19	—	—
1,000	6.31	4.68	2.95	2.00	—	3.24	2.45	1.66	1.19	—

4 Discussion

Based on the previous analysis, the accuracy of the proposed displacement estimation method may be affected by the following factors: strong earthquake recurrence interval T, b-value, minimum magnitude m ₀, upper limit m _uz of the fault magnitude, and the statistical relationship between magnitude and displacement distance.

4.1 b-Value

The b-value reflects the proportional relationship between the number of small earthquakes and large earthquakes in some areas. A larger b means a larger proportion of small-magnitude earthquakes in the earthquake series. In the same area, b-values calculated by different researchers may be different. Figure 2(a) shows the exceedance probability–displacement curves of b-values of 0.8 (red line) and 0.7 (green line). It can be observed that (1) when the b-value decreases from 0.8 to 0.7, the displacement (when the 100-year exceedance probability is 5%) increases by 3.5%; (2) the displacement distance and b-value are negatively correlated; (3) the difference was the largest at an exceedance probability of 2–4%, and the gap gradually decreases to both sides. On the premise that the global average b is approximately 1, the displacement calculated based on b = 0.8 is conservative and safe.

Figure 2

Effect of different parameters on the calculation results. (a) Different values of b (0.8 and 0.7), (b) different m ₀ values (7.0 and 6.8), (c) different m _uz values (8.0 and 8.5), and (d) different magnitude–displacement statistical relationships (regional and global) (circles and squares represent earthquakes in China and other countries, respectively).

4.2 Minimum magnitude m ₀ of generating surface displacements

Based on earthquake examples in the Chinese mainland, an earthquake with a magnitude of ≥7 will generate surface displacement. Huang [20] calculated the relationship between the magnitude and rupture of earthquakes and found that four earthquakes with magnitudes <7 had horizontal surface displacements. Figure 2(b) shows the m ₀ values of 7.0 (red line) and 6.8 (blue line). Under all exceedance probabilities, the smaller the m ₀ is, the smaller the displacement distance. Therefore, a m ₀ value of 7.0 is scientific and safe for structural design.

m ₀ = 7 is used in the calculation. However, earthquake damage around the world indicates that 6.0–6.9 magnitude earthquakes can also cause surface displacements. For instance, 1980 Mammoth Lake M _w 6.2 earthquake (e.g., the study of Clark and Yount [27]), 1980 Irpinia M _w 6.9 earthquake (e.g., the study of Bello et al. [28]), 1983 Borah Peak M _w 6.9 earthquake (e.g., the study of Bello et al. [29]), 1987 Edgecumbe M _w 6.2 earthquake (e.g., the study of Berrill et al. [30]), 2016 Parina M _w 6.1 earthquake (e.g., the study of Aguirre et al. [31]), and central Italy 2016 M _w 6.5 earthquake (e.g., the study of Brozzetti et al. [32]). It should be noted that m ₀ is influenced by different factors, such as the depth of the earthquake source and the thickness of the cover layer. In some regions around the world, 6.5 or even 6.0 magnitude earthquakes are more likely to cause surface displacements. In these cases, the interval of strong earthquakes revealed by surface trenching is the recurrence interval of 6.5 or 6.0 magnitude earthquakes. It is evident that the seismic hazard of an earthquake with a recurrence interval of T years at 6.5 magnitude is lower than that at 7.0 magnitude. In such cases, using m ₀ = 7.0 to assess surface displacement values may overestimate the risk.

4.3 Upper magnitude limit m _uz

The maximum earthquake magnitude occurring on the Holocene active fault is the upper magnitude limit. Based on the difference in the intensity of Holocene fault activity, the upper magnitude limit can be set to M7.5, M8.0, and M8.5. From the perspective of historical earthquakes, active faults within tectonic plates usually do not have the structural conditions to generate 8.6 or greater magnitude earthquakes. According to the historical seismic records in the Chinese mainland, the magnitude of the largest earthquake also did not exceed 8.5. Figure 2(c) shows the exceedance probability–displacement diagram of the upper magnitude limit at M8.5 (red line) and M8.0 (black line). It can be observed that, the lower the m _uz is, the smaller the surface displacement distance. However, this difference is not significant and only becomes significant when the probability of exceeding 100 years is less than 3%. M _w > 8 earthquakes often only occur at the first- or second-order plate boundaries, while M _w > 8.5 earthquakes often only occur at the first-order plate boundaries. Most of the active faults within the plate do not have the tectonic conditions required for earthquakes of magnitude ≥8.0, and m _uz = 8.5 is taken. The resulting surface displacement will exceed the actual surface displacement hazard values of the fault. If we use the surface displacement obtained from calculations in the structural design, the hazard of surface displacement will not be underestimated.

4.4 Sensitivity of parameters

Three seismic activity parameters, b-value, m ₀, and m _uz, are used in the calculation. To further analyze the impact of these parameters on the computational results, we calculate the sensitivity of the b-value, m ₀, and m _uz of an active fault with a strong earthquake recurrence interval of 1,000 years, assuming an exceedance probability of 4% within 100 years. The calculation results are shown in Figure 3. A decrease of 0.1 in b-value will increase to 0.08–0.22 m in surface displacement (Figure 3(a)); an increase of 0.1 in m ₀ will increase to 0.11–0.41 m in surface displacement (Figure 3(b)); an increase of 0.1 in m _uz will increase to 0.02–0.09 m in surface displacement (Figure 3(c)). The uncertainty of the b-value does not exceed 0.2, that of m ₀ can generally reach 0.5, and that of m _uz generally does not exceed 0.5. Therefore, the error in surface displacement caused by b-value and m _uz will not exceed 0.5 m, and that caused by m ₀ could reach 1–2 m. Therefore, when using this method to assess the hazard of surface displacement on active faults, special attention should be paid to the selection of m ₀.

Figure 3

Sensitivity of parameters: (a) b-value, (b) m ₀, and (c) m _uz.

4.5 Statistical relationship between magnitude and displacement distance

This parameter is the most important factor affecting the results of surface displacement hazard analysis. We compare the statistical relationship used with the statistical relationship of Wells and Coppersmith [33], the latter being the most widely used international model (Figure 2(d)). Figure 2(d) shows that there is a significant difference between the two groups. Taking an exceedance probability of 1% within 100 years as an example, the displacement distance calculated by the proposed statistical relationship is 6.3 m, and that using the Wells and Coppersmith [33] is 19.1 m, the latter being three times that of the former. The surface displacement distances of several 7–8 magnitude earthquakes in the Chinese mainland, Turkey, Japan, and the USA are as follows:

1920 Haiyuan M8.6 earthquake: its maximum horizontal displacement was 11 m [34];

1931 Fuyun Ms8 earthquake: its maximum horizontal displacement was 6.7 m, and its average horizontal displacement was 6.3 m [35];

2001 west Kunlun Ms8.1 earthquake: its maximum horizontal displacement was 6.4 m, and the maximum vertical displacement was 4 m [36];

2008 Wenchuan Ms8.0 earthquake: its maximum horizontal displacement was 6.8 m, with an average horizontal displacement of 3.1 m; its maximum vertical displacement was 6.2 m; with an average vertical displacement of 2.9 m [37];

2014 Yutian Ms7.3 earthquake: its maximum horizontal displacement was 0.9 m [38];

2021 Maduo Ms7.4 earthquake: its maximum horizontal displacement was 2.6 m [39];

1990 Philippines Ms7.8 earthquake: its maximum horizontal displacement was 6.2 m [33];

1992 Landers Ms7.6 earthquake: its maximum horizontal displacement was 6.0 m [33];

2023 eastern Turkey M _w 7.8 earthquake: its maximum horizontal displacement was 6.8 m [40];

2024 Noto Peninsula M _w 7.5 earthquake: its maximum displacement was 10 m [41].

These four earthquakes are shown in Figure 2(d) (under the premise that the strong earthquake recurrence interval of fault is 1,000 years and the b-value is 1). It can be seen from the locations in Figure 2(d) that the regional model used is suitable for the estimation of displacements in the Chinese mainland. In Figure 2(d), the squares indicate that the surface displacement distance of earthquakes in other countries significantly deviates from the proposed regional model. Therefore, if this method is used in the construction design of other countries to assess the future surface displacement hazard of active faults, it is necessary to choose the magnitude–displacement statistical relationship suitable for the project area; otherwise, it will lead to enormous errors.

4.6 Comparison with other probabilistic assessment methods

Youngs et al. [7] first proposed a probabilistic seismic displacement hazard assessment method for calculating the annual exceedance probability of a given displacement. Based on the PFDHA method, Moss and Ross [42] proposed a displacement probability analysis method for reverse faults. Petersen et al. [43] further studied this method and expanded the analysis for strike-slip faults. Subsequently, PFDHA was used to assess the future surface displacement hazard of faults. Compared with these methods, the proposed method has the following differences: First, we combine the displacement approach with the earthquake approach in PHDHA rather than choosing one method alone. From the perspective of geotechnical engineering, the displacement approach and the earthquake approach have their disadvantages. For example, the occurrence pattern of large earthquakes may deviate from the Gutenberg–Richter Law, and in geotechnical engineering, we are more concerned with the probability of large earthquakes. Second, we are not concerned with off-fault displacement on distribution faults. Off-fault deformation generally occurs over a wider range (100–300 m) and the displacement values are not significant, and its hazard is far less than the displacement on the principal fault. In seismic design codes, it is important to avoid major faults rather than distribution faults. Therefore, the displacements provided are all displacements on the main fault.

4.7 Limitations and future work

The parameters of recurrence intervals of strong earthquakes are used in the proposed method. If high-precision data are obtained on the recurrence intervals, the future surface displacement hazards can be accurately assessed. However, due to the reliability of dating methods, the uncertainty of stratigraphic ages, and the limited statistical analysis data, the recurrence interval data obtained may not be highly accurate. Addressing data uncertainty, future work might focus on studying the relationship between the recurrence interval from trenching and the recurrence interval from seismology.

Another limitation is that, like other surface displacement assessment methods, the results evaluated represent the maximum surface displacement distances. During a major earthquake, surface displacement may not occur along all segments of the fault; even in segments where surface displacement does occur, the values may vary significantly. For example, the maximum surface displacement in the 2021 Maduo M _w 7.4 earthquake was 2.6 m, but 30% of the area had no surface displacement, and 60% of the area had surface displacement values less than 1 m [39]. Therefore, evaluating the differential distribution of surface displacement and reasonably assessing the displacement values of structural locations may be a direction for future research.

5 Usage and examples

The usage is as follows:

The recurrence interval (T) of strong earthquakes near the structure site was exposed through trenches; the lateral angle of fault scratches was obtained through trenches and nearby fault sections.
Determine the fortification period of the project and convert it to the exceedance probability.
In Figure 4, the intersection point of the recurrence interval and the fortification exceedance probability are identified, and the horizontal displacement and vertical displacement of the fault can be calculated according to the vertical axis corresponding to the intersection point.
The total amount of displacements is calculated based on the horizontal displacement and the vertical displacement, and the total displacement is distributed in the horizontal and vertical directions according to the lateral angle of the scratches. If there are no data on the lateral angle, the data obtained in Step (3) can be used as the final result.

Figure 4

Exceedance probability–displacement curves of the active fault at different recurrence intervals: (a) horizontal displacement and (b) vertical displacement.

For example, when an oil pipeline passes through fault A, we excavate trenches near the intersection point. The recurrence interval of ancient earthquakes on the faults revealed by the trenches is 1,600 years. The lateral angle of the scratch is 20°. According to the importance of this pipeline, the recurrence periods that need to be obtained are 2,450 years (4% exceedance probability in 100 years) and 950 years (10% exceedance probability in 100 years).

In Figure 4, the year 1,580 is the closest to the year 1,600. The intersection points of the curve corresponding to 1,580 and x = 0.04 are 0.41 and 0.17, respectively. The calculated horizontal displacement and vertical displacement are 2.57 and 1.48 m, respectively. Based on this, the total displacement is calculated to be 2.9657 m. At a lateral angle of 20°, the horizontal displacement is 2.9657 × cos 20° = 2.79 m, and the vertical displacement is 2.9657 × sin 20 = 1.01 m. Therefore, on the time scale of 2,450 years return period, a horizontal displacement of 2.79 m and a vertical displacement of 1.01 m need to be considered. The curves corresponding to 1,580 and x = 0.10 have no intersection. Therefore, on the time scale of a 950-year return period, the surface displacements on active faults can be ignored.

The usages in other countries and regions are similar to those used in western China. That is, after consulting and calculating the horizontal displacement and vertical displacement of the fault, the results are converted to earthquake magnitudes according to equations (9) and (10). Then, based on the regional magnitude-surface displacement distance empirical relationships, the earth-quake magnitude is converted to new horizontal displacement and vertical displacement.

6 Conclusions

To summarize and absorb the results of previous studies, the data on the recurrence intervals of strong earthquakes on active faults and the classic probabilistic seismic hazard analysis method are used to achieve a general method for hazard analysis of probabilistic fault displacement.
Based on this method, the exceedance probability curves of the horizontal and vertical displacements of active faults with different recurrence intervals are calculated. The calculation results show that if the recurrence interval of strong earthquakes on a fault is longer than the return period considered of a structure, the influence of surface displacement on active faults can be ignored.
Exceedance probability–displacement curves of 27 recurrence intervals were calculated, and the diagrams were drawn (Figure 4). Designers can easily obtain vertical and horizontal displacements based on the recurrence interval of active faults and the recurrence period of seismic effects in engineering design. Designers from other countries and regions should ensure that the calculation parameters are consistent with our proposed ones before using the results. Otherwise, they should use the proposed method to recalculate or convert.
Parameters b-value and m _uz have a relatively minor impact on the assessment of surface displacement, while m ₀ and the magnitude–displacement empirical relationship has a significant influence on its assessment. If a small earthquake in a certain area can also cause surface displacement, or if the magnitude–displacement empirical relationship is substantially different from the relationship used here, the results should not be directly applied. On the contrary, the proposed method should be reapplied with appropriate parameters for new calculations.

zhou_1969321@163.com

Acknowledgments

The authors are grateful to the editor and the anonymous reviewers for their thorough and constructive reviews, which greatly improved the quality of this manuscript.

Funding information: This paper was funded by the Key Research and Development Plan of Yunnan Province (No. 202203AC100003), and Science and Technology Innovation Program of Yunnan Earthquake Agency (CXTD202408).
Author contributions: Qingyun Zhou performed methodology, formal analysis, and wrote the manuscript; Xianfu Bai performed funding acquisition, review, and editing; Jingnan Liu, Peng Tian, and Yue Yang participated in review. Weidong Luo and Zhenyu Zou revised the manuscript.
Conflict of interest: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
Data availability statement: All the data used in this article has been presented in the manuscript.

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Received: 2024-10-29

Revised: 2024-12-19

Accepted: 2025-01-07

Published Online: 2025-02-10

This work is licensed under the Creative Commons Attribution 4.0 International License.

Articles in the same Issue

https://doi.org/10.1515/geo-2022-0763

Keywords for this article

active fault; probabilistic fault displacement hazard analysis; strong earthquake recurrence interval; seismic design; return period

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BY 4.0

Hazard analysis of future surface displacements on active faults based on the recurrence interval of strong earthquakes

Article

Abstract

1 Introduction

2 Methods

2.1 Methods for estimating future displacements

2.2 Statistical relationship between surface displacements and magnitude

2.3 Method for the acquisition of strong earthquake recurrence interval

3 Results

4 Discussion

4.1 b-Value

4.2 Minimum magnitude m 0 of generating surface displacements

4.3 Upper magnitude limit m uz

4.4 Sensitivity of parameters

4.5 Statistical relationship between magnitude and displacement distance

4.6 Comparison with other probabilistic assessment methods

4.7 Limitations and future work

5 Usage and examples

6 Conclusions

Acknowledgments

References

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Articles in the same Issue

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4.2 Minimum magnitude m ₀ of generating surface displacements

4.3 Upper magnitude limit m _uz